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Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem

Rodriguez Ricard, Mariano; Mouhot, Clément; Mischler, Stéphane (2006), Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem, Journal of Statistical Physics, 124, 2-4, p. 655-702. http://dx.doi.org/10.1007/s10955-006-9096-9

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00087232/en/
Date
2006
Journal name
Journal of Statistical Physics
Volume
124
Number
2-4
Pages
655-702
Publication identifier
http://dx.doi.org/10.1007/s10955-006-9096-9
Metadata
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Author(s)
Rodriguez Ricard, Mariano
Mouhot, Clément
Mischler, Stéphane
Abstract (EN)
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness and instantaneous appearance of exponential moments are proved under additional smoothness assumption on the initial datum, for a restricted class of collision rates. Concerning the long-time behaviour, we give conditions for the cooling process to occur or not in finite time.
Subjects / Keywords
cooling process; Orlicz spaces; Cauchy problem; variable restitution coefficient; hard spheres; inelastic Boltzmann equation

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